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Towards a symplectic cycle theory: the Lagrangian Ceresa cycle

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If you have a question about this talk, please contact Dhruv Ranganathan .

I will begin with a general introduction to some of the ideas I am interested in, for which a guiding motivation is to understand a “Lagrangian version” of the theory of algebraic cycles (Chow groups, Griffiths groups, etc), as suggested by mirror symmetry. I will present an instance in which algebraic behaviour can be recovered symplectically, by a Lagrangian version of the classical Ceresa cycle story. The Ceresa cycle of a curve is a 1-cycle in its Jacobian and provided one of the first examples of a homologically trivial cycle which is not algebraically trivial. The Lagrangian construction involves the tropical version of the Ceresa cycle story, due to Zharkov. It also requires introducing an equivalence relation on Lagrangians ‘mirror’ to algebraic equivalence, called algebraic Lagrangian cobordism.

This talk is part of the Algebraic Geometry Seminar series.

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Average on weekdays: 8928.88240918 kWh Large Lecture Theatre, Department of Geography Online, Zoom TBC

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